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Transcript determine-sig
DETERMINING SIGNIFICANT
FIGURES
CRUNCHING NUMBERS WITH ACCURACY
AND PRECISION
BEFORE YOU CAN CRUNCH
2
You must know which digits are significant
Because they are going to control the number of
digits in a calculated figure
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WHAT IS A SIGNIFICANT FIGURE?
3
Significant figures are all the digits in a measurement
that are known with certainty plus a last digit that
must be estimated.
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WHICH NUMBERS ARE SIGNIFICANT?
4
For the purposes of significant figures there are two
major categories
Nonzero digits:
1,2,3,4,5,6,7,8,9
Zero digits:
0
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5
NONZERO
DIGITS
All nonzero digits are significant
3269 cm – 4 significant figures
257 L – 3 significant figures
1.234567 mm – 7 significant figures
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6
ZEROES
Zeroes take three forms
Leading zeroes
Trapped zeroes
Trailing zeroes
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LEADING7 ZEROES
Leading zeroes are zeroes that come before the
nonzero digits in a number. They are place holders
only and are never considered significant.
0.123 L – 3 significant digits
0.000012 m – 2 significant digits
0.003578 mL – 4 significant digits
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TRAPPED8 ZEROES
Trapped zeroes are zeroes between two nonzero
digits. Trapped zeroes are always significant.
101 s – 3 significant figures
20013 m – 5 significant figures
0.3006 cm – 4 significant figures (the
leading zero is not significant)
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TRAILING9 ZEROES
Trailing zeroes are zeroes that follow nonzero digits.
They are only significant if there is a decimal point in
the number.
0.1200 mm – 4 significant figures
3000 s – 1 significant figure
250. mL – 3 significant figures
50.000 g – 5 significant figures
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10
Exact Numbers
Numbers that were not obtained using measuring
devices but by counting.
They can also arise from definitions.
They can be assumed to have an infinite number of
significant figures.
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Examples of Exact Numbers
11
2 in 2r
3 and 4 in ¾ r3
Avogadro’s number is exactly
6.02 x 1023
One inch is exactly 2.54 cm
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Now you try
12
How many significant digits in each of the following:
1.034 s
0.0067 g
12 apples
3000 m
69 people
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Answers
13
1.034 s
- 4 significant figures
0.0067 g - 2 significant figures
12 apples - exact number
3000 m - 1 significant figure
69 people - exact number
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